Finite Group DatabasebetaFinite Group Databasebeta| order | 32364 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C31⋊C3×#1181 |
| unambiguous semidirect product | (C31×#1181)⋊C32 |
| unambiguous semidirect product | (C3×C31×#1181)⋊C3 |
| Fitting, socle | C3×C29×C31 ⋊ C3×C4 |
| derived, Hall | C29×C31 ⋊ C32×C4 |
| Hall | C3×C29×C31⋊C3 ⋊ C4 |
| Hall | C31×#1181 ⋊ C32 |
| Sylow | C31 ⋊ C32×#1181 |
| Sylow | C29 ⋊ C3×C4×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C31⋊C3×#1181 |
| commutator, hypocenter | C29×C31 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C31 | C3×C4 |
| prime radical | C3×D29×C31⋊C3 | C2 |
| cosocle | C31×D29 | C2×C32 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2697 |
429 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32364, 63);